IEICE TRANSACTIONS on Communications
Wigner's Semicircle Law of Weighted Random Networks
Summary :
Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.
- Publication
- IEICE TRANSACTIONS on Communications Vol.E104-B No.3 pp.251-261
- Publication Date
- 2021/03/01
- Publicized
- 2020/09/01
- Online ISSN
- 1745-1345
- DOI
- 10.1587/transcom.2020EBP3051
- Type of Manuscript
- PAPER
- Category
- Fundamental Theories for Communications
Authors
Yusuke SAKUMOTO
Kwansei Gakuin University
Masaki AIDA
Tokyo Metropolitan University
Keyword
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Yusuke SAKUMOTO, Masaki AIDA, "Wigner's Semicircle Law of Weighted Random Networks" in IEICE TRANSACTIONS on Communications,
vol. E104-B, no. 3, pp. 251-261, March 2021, doi: 10.1587/transcom.2020EBP3051.
Abstract: Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.2020EBP3051/_p
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@ARTICLE{e104-b_3_251,
author={Yusuke SAKUMOTO, Masaki AIDA, },
journal={IEICE TRANSACTIONS on Communications},
title={Wigner's Semicircle Law of Weighted Random Networks},
year={2021},
volume={E104-B},
number={3},
pages={251-261},
abstract={Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.},
keywords={},
doi={10.1587/transcom.2020EBP3051},
ISSN={1745-1345},
month={March},}
Copy
TY - JOUR
TI - Wigner's Semicircle Law of Weighted Random Networks
T2 - IEICE TRANSACTIONS on Communications
SP - 251
EP - 261
AU - Yusuke SAKUMOTO
AU - Masaki AIDA
PY - 2021
DO - 10.1587/transcom.2020EBP3051
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E104-B
IS - 3
JA - IEICE TRANSACTIONS on Communications
Y1 - March 2021
AB - Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.
ER -
English
